This invention relates to multi-layer walls for building purposes formed of aluminum or plastic extrusions which may be snapped together to form, when assembled in proper sequence, insulated, sound-proof inside and outside wall structures which support ceiling and floors of a multi-story building structure. More particularly, this invention is directed to novel multi-layer walls formed from only a few different extruded structural elements which are pre-cut, formed and shaped to fit together in an interlocking manner with a minimum of tools to form a variety of frameless, multi-story buildings which may be used for home, office, business, church or other building use.